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They are applied to determine the injective chromatic number of Sierpi\u0144ski graphs and to give a short proof that Sierpi\u0144ski graphs are Class 1. Sierpi\u0144ski-like graphs are also considered, including generalized Sierpi\u0144ski graphs over cycles and rooted products. It is proved that the injective chromatic number of a rooted product of two graphs lies in a set of six possible values. Sierpi\u0144ski graphs and Kneser graphs <jats:italic>K<\/jats:italic>(<jats:italic>n<\/jats:italic>,\u00a0<jats:italic>r<\/jats:italic>) are considered with respect of being perfect injectively colorable, where a graph is perfect injectively colorable if it has an injective coloring in which every color class forms an open packing of largest cardinality. 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